A token is hidden in one of several boxes and then the boxes are locked. The probability of placing the token in each of the boxes is known. A searcher is looking for the token by unlocking boxes where each box is associated with an unlocking cost. The searcher conducts its search in rounds and must find the token in a predetermined number of rounds. In each round, the searcher may unlock any set of locked boxes concurrently. The optimization goal is to minimize the expected cost of unlocking boxes until the token is found. The motivation and main application of this game is the task of paging a mobile user (token) who is roaming in a zone of cells (boxes) in a Cellular Network system. Here, the unlocking costs reflect cell congestions and the placing probabilities represent the likelihood of the user residing in particular cells. Another application is the task of finding some data (token) that may be known to one of the sensors (boxes) of a Sensor Network. Here, the unlocking cos...